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Simplifying 3(x + -2)(x + 1) + (x + 4)(x + 2) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) Reorder the terms: 3(-2 + x)(x + 1) + (x + 4)(x + 2) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) Reorder the terms: 3(-2 + x)(1 + x) + (x + 4)(x + 2) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) Multiply (-2 + x) * (1 + x) 3(-2(1 + x) + x(1 + x)) + (x + 4)(x + 2) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) 3((1 * -2 + x * -2) + x(1 + x)) + (x + 4)(x + 2) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) 3((-2 + -2x) + x(1 + x)) + (x + 4)(x + 2) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) 3(-2 + -2x + (1 * x + x * x)) + (x + 4)(x + 2) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) 3(-2 + -2x + (1x + x2)) + (x + 4)(x + 2) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) Combine like terms: -2x + 1x = -1x 3(-2 + -1x + x2) + (x + 4)(x + 2) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) (-2 * 3 + -1x * 3 + x2 * 3) + (x + 4)(x + 2) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) (-6 + -3x + 3x2) + (x + 4)(x + 2) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) Reorder the terms: -6 + -3x + 3x2 + (4 + x)(x + 2) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) Reorder the terms: -6 + -3x + 3x2 + (4 + x)(2 + x) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) Multiply (4 + x) * (2 + x) -6 + -3x + 3x2 + (4(2 + x) + x(2 + x)) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) -6 + -3x + 3x2 + ((2 * 4 + x * 4) + x(2 + x)) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) -6 + -3x + 3x2 + ((8 + 4x) + x(2 + x)) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) -6 + -3x + 3x2 + (8 + 4x + (2 * x + x * x)) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) -6 + -3x + 3x2 + (8 + 4x + (2x + x2)) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) Combine like terms: 4x + 2x = 6x -6 + -3x + 3x2 + (8 + 6x + x2) = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) Reorder the terms: -6 + 8 + -3x + 6x + 3x2 + x2 = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) Combine like terms: -6 + 8 = 2 2 + -3x + 6x + 3x2 + x2 = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) Combine like terms: -3x + 6x = 3x 2 + 3x + 3x2 + x2 = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) Combine like terms: 3x2 + x2 = 4x2 2 + 3x + 4x2 = 5(x + -1)(x + -1) + -1x + -1x + 3(x + -6) Reorder the terms: 2 + 3x + 4x2 = 5(-1 + x)(x + -1) + -1x + -1x + 3(x + -6) Reorder the terms: 2 + 3x + 4x2 = 5(-1 + x)(-1 + x) + -1x + -1x + 3(x + -6) Multiply (-1 + x) * (-1 + x) 2 + 3x + 4x2 = 5(-1(-1 + x) + x(-1 + x)) + -1x + -1x + 3(x + -6) 2 + 3x + 4x2 = 5((-1 * -1 + x * -1) + x(-1 + x)) + -1x + -1x + 3(x + -6) 2 + 3x + 4x2 = 5((1 + -1x) + x(-1 + x)) + -1x + -1x + 3(x + -6) 2 + 3x + 4x2 = 5(1 + -1x + (-1 * x + x * x)) + -1x + -1x + 3(x + -6) 2 + 3x + 4x2 = 5(1 + -1x + (-1x + x2)) + -1x + -1x + 3(x + -6) Combine like terms: -1x + -1x = -2x 2 + 3x + 4x2 = 5(1 + -2x + x2) + -1x + -1x + 3(x + -6) 2 + 3x + 4x2 = (1 * 5 + -2x * 5 + x2 * 5) + -1x + -1x + 3(x + -6) 2 + 3x + 4x2 = (5 + -10x + 5x2) + -1x + -1x + 3(x + -6) Reorder the terms: 2 + 3x + 4x2 = 5 + -10x + 5x2 + -1x + -1x + 3(-6 + x) 2 + 3x + 4x2 = 5 + -10x + 5x2 + -1x + -1x + (-6 * 3 + x * 3) 2 + 3x + 4x2 = 5 + -10x + 5x2 + -1x + -1x + (-18 + 3x) Reorder the terms: 2 + 3x + 4x2 = 5 + -18 + -10x + -1x + -1x + 3x + 5x2 Combine like terms: 5 + -18 = -13 2 + 3x + 4x2 = -13 + -10x + -1x + -1x + 3x + 5x2 Combine like terms: -10x + -1x = -11x 2 + 3x + 4x2 = -13 + -11x + -1x + 3x + 5x2 Combine like terms: -11x + -1x = -12x 2 + 3x + 4x2 = -13 + -12x + 3x + 5x2 Combine like terms: -12x + 3x = -9x 2 + 3x + 4x2 = -13 + -9x + 5x2 Solving 2 + 3x + 4x2 = -13 + -9x + 5x2 Solving for variable 'x'. Reorder the terms: 2 + 13 + 3x + 9x + 4x2 + -5x2 = -13 + -9x + 5x2 + 13 + 9x + -5x2 Combine like terms: 2 + 13 = 15 15 + 3x + 9x + 4x2 + -5x2 = -13 + -9x + 5x2 + 13 + 9x + -5x2 Combine like terms: 3x + 9x = 12x 15 + 12x + 4x2 + -5x2 = -13 + -9x + 5x2 + 13 + 9x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 15 + 12x + -1x2 = -13 + -9x + 5x2 + 13 + 9x + -5x2 Reorder the terms: 15 + 12x + -1x2 = -13 + 13 + -9x + 9x + 5x2 + -5x2 Combine like terms: -13 + 13 = 0 15 + 12x + -1x2 = 0 + -9x + 9x + 5x2 + -5x2 15 + 12x + -1x2 = -9x + 9x + 5x2 + -5x2 Combine like terms: -9x + 9x = 0 15 + 12x + -1x2 = 0 + 5x2 + -5x2 15 + 12x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 15 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + -12x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -12x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -12x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -12x + x2 = 0 + 15 -12x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -12x + x2 = 15 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 15 + 36 Reorder the terms: 36 + -12x + x2 = 15 + 36 Combine like terms: 15 + 36 = 51 36 + -12x + x2 = 51 Factor a perfect square on the left side: (x + -6)(x + -6) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + -6) equal to 7.141428429 and -7.141428429.Subproblem 1
x + -6 = 7.141428429 Simplifying x + -6 = 7.141428429 Reorder the terms: -6 + x = 7.141428429 Solving -6 + x = 7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.141428429 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.141428429 + 6 x = 7.141428429 + 6 Combine like terms: 7.141428429 + 6 = 13.141428429 x = 13.141428429 Simplifying x = 13.141428429Subproblem 2
x + -6 = -7.141428429 Simplifying x + -6 = -7.141428429 Reorder the terms: -6 + x = -7.141428429 Solving -6 + x = -7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.141428429 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.141428429 + 6 x = -7.141428429 + 6 Combine like terms: -7.141428429 + 6 = -1.141428429 x = -1.141428429 Simplifying x = -1.141428429Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.141428429, -1.141428429}
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